Neyman-Pearson Lemma

#1
I am having trouble on finding. K.
Ex: given sample size n=1 for geometric didn't. Use NP to find critical region H0:x=x0. Ha :x1>x0
L0/L1=x0/x1((1-x0)/(1-x1))^y-1 <k
Since x1>x0 monotone decreasing and L0/L1<1
Since this the geometric dist , it is based off geometric sequence so the function that maximizes it
is
Sum [n=1 to c] ar^n=x0(1-x0^c)/(1-x0)=

Suppose n>1 what then ?